On equalities in two entropic inequalities

Abstract

A simple criterion for local equality between the constrained Holevo capacity and the quantum mutual information of a quantum channel is obtained. It implies that the set of all states for which this equality holds is determined by the kernel of the channel (as a linear map). Applications to Bosonic Gaussian channels are considered. It is shown that for a Gaussian channel having no completely depolarizing components the above characteristics may coincide only at non-Gaussian mixed states and a criterion of existence of such states is given. All the obtained results may be reformulated as conditions for equality between the constrained Holevo capacity of a quantum channel and the input von Neumann entropy.

23 pages, any comments are welcome

References in corpus (7)

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• Multi-mode bosonic Gaussian channels
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• On the entanglement-assisted classical capacity of infinite-dimensional quantum channels
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